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C₁₉×C₅⋊(#4294⋊C₂) #44570470

order	32490
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×C₅⋊(#4294⋊C₂)
unambiguous semidirect product	C₅⋊(C₁₉×#4294⋊C₂)
unambiguous semidirect product	#4294⋊(D₅×C₁₉)

Splittings

derived	C₅×C₁₉ ⋊ C₂×C₉×C₁₉
Hall	C₅×C₁₉×#4294 ⋊ C₂
Hall	C₁₉×D₉₅ ⋊ C₉
Hall	C₁₉×#4294 ⋊ D₅
Hall	C₅×C₁₉² ⋊ C₂×C₉
Sylow	C₁₉² ⋊ C₉×D₅
Sylow	C₅ ⋊ C₁₉×#4294⋊C₂

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₉	C₅⋊(D₁₉⋊C₃)
commutator, hypocenter	C₅×C₁₉	C₂×C₉×C₁₉
Frattini	C₃	C₁₉×C₅⋊(D₁₉⋊C₃)
Fitting, socle	C₃×C₅×C₁₉²	C₂×C₃
prime radical	C₃×C₁₉×D₉₅	C₃
cosocle	C₃×C₅×C₁₉	C₂×C₃×C₁₉
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₃×C₁₉

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1710

Conjugacy classes & character table

1539 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32490, 54);